Question

For each of the problems below solve for monopoly quantity, monopoly price, total revenue, total cost, profit, and dead weight loss.

a. Qd = 100 – 0.5p                           TC = 2Q²

b. Qd = 500 – 0.2p TC = Q² + 100Q

c. Qd = 30 – 0.6p                             TC = Q² + 10Q +100

d. Qd = 1000 – 0.25p                       TC = 2Q² + 25Q + 100

Answer 1

a Qd = 100- 0.5P Now, invu se demand 100-Qd = 0.5 P . =) 200 - 2 Qd =P Total revenue (TR) PQd = (200-2Qd)? = 200 Qd = 2 Qd² - dCTR)_ 200-4 Qd. - dad Marginal revenue (MR) == ALSO TO = २९- २९- Marginal cost MC = d (TC) = 4 Qd. A dQd condition Now profit mani mizing c) MR = MC =) 200-4 Qd = 4 Qd =) - 9Qd = - 200 Qd = 2547 Monopoly Price p= 200-2 Qd. = 20-2(25) = 200-5o = $150 Total revenue = (PX Qd) & (150825) 59 3750 Total cost = 20 = 2 (252 = $ 1250

Profit T = Total revenue - Total cost = $ (3750 - 1250) - $ 2500 Now, p= 200-2 ad When po, Qd = 100 When Qdzo p= 200 Marginal revenue MR = 200-4 Qd. when Qd =0 MRE 200 When Qd =0 MA Qd = 50 When a MR=0 Also Me= 4 Qd ме Price a 150 ft 100 + Demand 25 so 100 Quantity deadweight loss is the area AABC point B. we substitute the deadweight lo Now, act MR equation. MR= 200- 4Qd Qd =25, in Thes, CX = 200 - 4(25) = $180

To get point ce we equation 2 P= MC MC = 4Qd we know Qd = 25 So Mc'- 25×4 = 6100 Now P= mc boo implin 200-2 Qd = 100 100 = 2Qd Qd = 50 This deadweight loss will be - Area of ABC 1 x ( 50-25)x (150-10) CS Scanned with - 1 x 95 x 50 =$625 CamScanner

b) Qd = 500-012P TC=Q² + 1000Q TC=Q² + 100 Q b Qd = 500- 0.2P =) Now, ad = 500-0.2P = 500- Qd = 0.2P 2500 - 5Qd = pi Total revenue = P Qd = 12500-5Qd) Qd = 2500 Qd - 502 Marginal revenue (MR) = 2500 - 10 Qd Also, TC = Q2 + 100Q Mc = 2Q 7 100 Now MR = mc implin 2500-10 Qd = 2 Qd + 100 - 12 Qd = - 2400 = Qd = 200 Pure will be p= 2500-5Qd = 2500 - 5(200) = 2500 - 1000 - 1500 To t to tu Лисимо wе мира ръyq. This Total revenue (PQd). = 9(1500 x 200) =$ 300,00 Scanned with CamScanner

To tal cost of an To - Q²+ 100Q - (200) 27100(200) :-$60,000 Profit will be a TR- TC) =47300,000 - 60,000) $ 240, oor. I Now, Qd = 500 -0.2P when p=0 Qd = 500 when Qd =0, P = 2500 NOW, MR = 2500-10Qd when Qd =0 MR = 2500 When MR =O Qd = 250 Also, mc= 20 +100

Puce mo sa MC =2Qtlo 2500 1500 500 100 MR 200 250 S . Фuox8* is the area of A ABC Scanned with loss Dead brught.

Now, to get point 'B' we substitute Qd=200 in the MR function Tus, MR = 2500-10Qd ) = 2500 – 10 (200) 2 500 Now. Deadweight loss = { x (1500-500) X (P50-20 25,000 Scanned with CamScanner

Te= Q 7 1004100 C) Qd = 30-0.6P Now Qd = 30-0.6 P. =) 30-Q d = 0.6P =) 50 - 1.66 Qd = p. Now Total revenue . TR = P Qd = 50 Qd - 1.66 Qd² MR = 50-3.32 Qd Te = au + 100 + 100 MC = 2 Qd +10 Now equating MRMCA 50- 3 3 2 Qd = 2 Qdt10 Dan - 5132 Qd = -40 Qd = 7.52 tp he cm 50-1.66 al p = Pure 50- 1.66 Qd = 50 – 1.66 (7,52 = 37,52 1.52) ou Total Now revenue = P Qd = 67,52 X 7152) - 28215 Scanned with CamScanner

Totul cost Qud + load +100 = 1715273+1017152)+100 = $ 231.75 profit will be = TR-TC I - $ (2 82.15 - 232.15) = $50 Now Qd = 30-0.6P when p=0=) Qd = 30 when ad=0 =) P = 50 Now MR = 50- 3.32 Qd. when Qd = 0 => MR=50 gas is 15 MR =0 =% when MC = 2Qd +10 MC =2Qd +10 Jot 37152 AAA Bl 25 naud 10 t MR 7152 is 30 Scanned with CamScanner

Now to get Substitute equation point Qd- & we 7.52 in MR They MR = 50-3.32 Qd = so- 3.32 (7152) = 25 Thes, Deadweight loss... = Area of A ABC = Ź X (15- 7152) x(37.52–25) 2 X 7:48 x 12:52 = $ 4682 d Qd = 1000 - 0.25 p Now, 12000 - Qd = 0.25 p 4 000 - 4Qd = p. Total revenue (PQd = 4 orood -4 Qd TA= Marginal revenues ? inal revenue = 2000-8 Qd TE= 20 2t 25Qdt 100 Mc = 4Qd725 Now,

Equating MR = me we get 0675 l 4000-8Qd = 4Q tas - - 12 Qd - 3975 =) Qd = 331.25 Now p= 4000 - 4Qd. - 4000 - 41351.95) = $2675 Now to tal revenue & PQd. = 9(2675 X 33).45).) =886,093.75 Profit - TR TE Total cost = 2 Q8 tas Qat 100 = 2 (331-25)?+25 (337.25) +100 3 219,45311278781.25+100 = R 27,834.37 Now Profit (11) = (886,093,75 - 227,834.37) - TC. $658,259.38 poder AM

Now I Qd = 1000 - 0.25 P When Qd = 0, P= $4000 when p=0 => Qd = 1000 osti MR= 4000 - 8 Qd When Qd =0, MR 4000 When MR = 0 Qd = 500 Also Mc = 4 Qd tas Price of mc=40dtas 4ook 2675 1350 Dumond MA 331.25 50 100 Quantity substitute Qd = 331,25 To get B' we substitute a in MR function Hnce MR = 4000-8 (331,25). - 1350

Now, Deadweight loss - Area of A ABC - { x ( 500- 33).25) X (2675-1350) = { x 168.95 x 13.85 = $ 111,929.38 Sanped with